Learning latent variable structured prediction models with Gaussian perturbations

TL;DR

This paper introduces a novel approach for structured prediction models with latent variables using Gaussian perturbations, providing theoretical analysis and practical algorithms that improve learning efficiency and generalization bounds.

Contribution

It extends existing random sampling methods to include latent variables, offering a tighter upper bound on Gibbs decoder distortion and faster evaluation techniques.

Findings

The method achieves tighter bounds on model distortion.

It demonstrates improved efficiency in learning with latent variables.

Experimental results validate the theoretical advantages.

Abstract

The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work has proposed the use of the maximum loss over random structured outputs sampled independently from some proposal distribution, with theoretical guarantees. We extend this work by including latent variables. We study a new family of loss functions under Gaussian perturbations and analyze the effect of the latent space on the generalization bounds. We show that the non-convexity of learning with latent variables originates naturally, as it relates to a tight upper bound of the Gibbs decoder distortion with respect to the latent space. Finally, we provide a formulation using random samples that produces a tighter upper bound of the Gibbs decoder distortion up to a statistical accuracy, which enables a faster evaluation of the objective function. We illustrate the method with synthetic experiments and a computer vision application.